Complex Network is a mathematical model applied in several practical problems, such
as airplane routes between airports, connections between subway stations, interactions
in social networks, bibliographic citations in articles, scientific projects, and even in in-
teractions between neural network proteins. The study of complex networks consists of
understanding how each element of this network relates to the others, as well as the be-
havior of the network as a whole. Graphs are the mathematical tool used to model these
real networks, therefore studies of this theory are necessary. For this, we will make an
introductory bibliographical study about graph theory, presenting a brief history of the
Könisgberg Bridge Problem and Euler’s solution that started Graph Theory, the basic
definitions about the elements of a graph and about some graph types. We will also
present the definitions of some elements and types of Networks, the topologies of Regular
Networks, Random Networks, Small World Network Model and Scale Free Networks. And
finally, we will present the following measures used in the characterization of networks:
the Measures of Connectivity, Measures related to Cycles, Measures of Distances and
Measures of Centralities
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